Definition of Function
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Q. If a+α=1, b+β=2 and af(x)+αf(1x)=bx+βx, x≠0, then the value of the expression f(x)+f(1x)x+1x is
Q. Which among the following relations defined on R is/are functions
![](https://search-static.byjusweb.com/question-images/byjus/ckeditor_assets/pictures/1029417/original_122.JPG)
- (i)
- (ii)
- (iv)
- (v)
Q. Which among the following is/are odd functions?
- g(x)=ax−1ax+1
- f(x)=x(ex−1ex+1)
- h(x)=log(x6+√x2+1)
- k(x)=x(x2−|x|)
Q. If f:N→N, where N is set of natural numbers and f(xy)=f(x)⋅f(y)−f(x+y)+1 ∀x, y∈N and f(1)=2, then the value of 1+∞∑k=1f(k)2k is
Q. Let A and B be two sets such that n(A)=6 and n(B)=3, then number of onto functions from A to B is
Q. If f:[12, ∞)→[34, ∞) given by f(x)=x2−x+1, then f−1(x)=
- 12+√x−14
- 14+√x−12
- 12+√x−34
- 12−√x−34
Q. Let R be a relation on a set A such that R=R−1, then R is
- a reflexive relation
- a symmetric relation
- a transitive relation
- None of the above
Q. Which of the following is not a function?
Q. If the 10th term of an A.P. is 35 and the 5th term is 20, then
- a=9
- d=3
- a=8
- T9=32
Q. Which among the following is\are function(s)
Q. Which of the following is/are functions?
Q. Which of the following is/are a function?
Q. Let A={x1, x2, x3, x4, x5, x6} and f:A→A. The number of bijective functions such that f(xi)=xi for exactly four of the xi is
Q. Which of the following functions is inverse to itself?
- f(x)=1−x1+x
- f(x)=5logx
- f(x)=sinx
- f(x)=2x(x−1)
Q. If n(A)=n, n>0 then which among the following statements are correct
- Number of relations on A that are not reflexive =(2n2−n)(2n−1)
- Number of relations on A that are not reflexive =(2n2+n)(2n−1)
- Number of relations on A that are not symmetric
=2n2−2n(n+1)2 - Number of relations on A that are not symmetric
=2n2−2n(n−1)2